An Elementary Treatise on Algebra: Theoretical and Practical ... |
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Page 10
... coefficient , thus 3x , 3 is the coefficient of a , and indicates that three a's are taken . Coefficients may ... coefficients of x . ( 11 ) A measure of any quantity is that by which it can be divided without a remainder . 2 is a ...
... coefficient , thus 3x , 3 is the coefficient of a , and indicates that three a's are taken . Coefficients may ... coefficients of x . ( 11 ) A measure of any quantity is that by which it can be divided without a remainder . 2 is a ...
Page 12
... coefficients , but a cannot be added to b , or 4a to 36 , or to any other dissimilar quantity , because it would be adding unlike things , but we can write a + b and 3a + 3b , indicating the addition by the sign , making a compound ...
... coefficients , but a cannot be added to b , or 4a to 36 , or to any other dissimilar quantity , because it would be adding unlike things , but we can write a + b and 3a + 3b , indicating the addition by the sign , making a compound ...
Page 13
... coefficients into one sum and the negative ones into another , and take their difference with the sign of the greater , to which prefix the common literal quantity . EXAMPLES FOR PRACTICE . 5a 17x + 5ab 6a + 56-7cd + 8xy 2a 2x -6ab -6a ...
... coefficients into one sum and the negative ones into another , and take their difference with the sign of the greater , to which prefix the common literal quantity . EXAMPLES FOR PRACTICE . 5a 17x + 5ab 6a + 56-7cd + 8xy 2a 2x -6ab -6a ...
Page 14
Theoretical and Practical ... Horatio Nelson Robinson. their coefficients , and then write the different sums , one after another , with their proper signs . EXAMPLES . Bay 9x2y 2ax -Бху -7x2y + Заху бах Ax2y 2 Sum Sax - 2xy Заху - 2x2y ...
Theoretical and Practical ... Horatio Nelson Robinson. their coefficients , and then write the different sums , one after another , with their proper signs . EXAMPLES . Bay 9x2y 2ax -Бху -7x2y + Заху бах Ax2y 2 Sum Sax - 2xy Заху - 2x2y ...
Page 15
... coefficients we may add them by putting their coefficients in a vinculum and writing the term on the outside as a factor . Thus the sum of ax and bx is ( a + b ) x . EXAMPLES . Add ax + by3 2cx + 3ay2 4dx + 7y2 ay + cx Зау + 2сх ( 4a + ...
... coefficients we may add them by putting their coefficients in a vinculum and writing the term on the outside as a factor . Thus the sum of ax and bx is ( a + b ) x . EXAMPLES . Add ax + by3 2cx + 3ay2 4dx + 7y2 ay + cx Зау + 2сх ( 4a + ...
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An Elementary Treatise on Algebra: Theoretical and Practical Horatio Nelson Robinson No preview available - 2016 |
Common terms and phrases
2d power 3d term 4th power added algebraic arithmetical arithmetical mean arithmetical series assumed binomial square cent Clearing of fractions coefficients common difference Completing the square compound interest compound quantity cube root cubic equation distance Divide the number dividend division divisor dollars equa equal roots equation becomes EXAMPLES Expand exponents factors find the values following rule four numbers fourth fraction will produce geometrical progression geometrical series give greater greatest common measure Hence improper fraction last term least common multiple less letter logarithm lowest terms method miles mixed quantity moon number of terms numbers in geometrical Observe operation primitive equation principle problem produce the series quadratic equations quotient remainder represent Required resolved second power shillings simple equations solution square root substitute subtract suppose Theorem third three numbers tion Transpose unknown quantity unknown term whole numbers
Popular passages
Page 11 - If equal quantities be divided by the same, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 33 - To reduce a mixed quantity to an improper fraction, multiply the integer by the denominator of...
Page 195 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means as 7 to 3. What are the numbers?
Page 184 - If the sum of an arithmetical series is 567, the first term 7, and the common difference 2; what is the number of terms?
Page 202 - There are two numbers, which are to each other, as 16' to 9, and 24 is a mean proportional between them. What are the numbers ? Ans. 32 and 18. 13. The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to the greater as 102 to 5. What are the numbers 1 Ans.
Page 145 - Prob. 9. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16.
Page 42 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 155 - Any trinomial can be separated into two binomial factors, when the extremes are squares and positive, and the middle term is twice the product of the square roots of the extremes.
Page 191 - When three magnitudes, a, b, c, have the relation of a: c: : a—b : b—c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 143 - A and B, set out to meet each other; A leaving the town C at the same time that B left D. They travelled the direct road...